Applications of probability

This module introduces models to describe patterns of events that occur in time (such as earthquakes), and in space (for instance, the occurrence of a species of plant). Situations that occur only at discrete time points, including the ruin of a gambler, are studied. Probability models are developed for those situations, such as the spread of an epidemic, in which events may occur at any time. The module ends with other situations involving probability including genetics and changes in stockmarket prices. You are expected to be reasonably competent in calculus and algebra.

Modules count towards OU qualifications

OU qualifications are modular in structure; the credits from this undergraduate-level module could count towards a certificate of higher education, diploma of higher education, foundation degree or honours degree.

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What you will study

This module in probability and its applications emphasises probability modelling and developing the properties of the models. A considerable amount of mathematics is sometimes required for this development, but we do not always give formal proofs, particularly if the proof does not illuminate the probabilistic ideas.

The module consists of six books.

The first one, which is introductory, revises and develops ideas about probability and introduces some techniques that will be used frequently in the module.

The second book develops models for events occurring in time, including the Poisson process and several extensions of it, and patterns in space, including models for random scatter and clustering of objects.

The third book develops models for processes in which events can occur only at discrete time points, such as a Bernoulli process. This includes practical situations such as the ruin of a gambler and the extinction of a family surname.

In the fourth book, probability models are developed for situations in which events can occur at any time. Examples include queues, the spread of epidemics, and the change in the size of a population due to births and deaths.

In the fifth book, models are developed for various situations, including genetics, the renewal of components, and the change in stock market prices.

Computer simulations are used to illustrate some of the phenomena studied, and associated activities are included in a separate book.

Professional recognition

This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.

Teaching and assessment

Support from your tutor

You will have a tutor who will help you with the study material and mark and comment on your written work, and whom you can ask for advice and guidance. We may also be able to offer group tutorials or day schools that you are encouraged, but not obliged, to attend. Where your tutorials are held will depend on the distribution of students taking the module.

Contact us if you want to know more about study with The Open University before you register.

Assessment

The assessment details for this module can be found in the facts box above.

Please note that tutor-marked assignments (TMAs) for all undergraduate mathematics and statistics modules must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system.

Future availability

The details given here are for the module that starts in October 2015. We expect it to be available once a year.

Regulations

As a student of The Open University, you should be aware of the content of the Module Regulations and the Student Regulations which are available on our Essential documents website.

Course work includes:

3 Tutor-marked assignments (TMAs)

4 Interactive computer-marked assignments (iCMAs)

Examination

No residential school

Course satisfaction survey

Entry

This is an OU level 3 module. OU level 3 modules build on study skills and subject knowledge acquired from studies at OU levels 1 and 2. They are intended only for students who have recent experience of higher education in a related subject, preferably with the OU.

You are expected to have a basic knowledge of probability: probability functions for discrete random variables and probability density functions for continuous random variables; the binomial, Poisson, geometric, exponential and normal distributions; the Poisson process.

Analysing data (M248) would be ideal preparation but, if you have not studied this module, a revision of the rules of probability and some basic probability models is included in the first book. We recommend that you study this as early as you can so that you are prepared for the rest of the module.

You are also expected to have a reasonable degree of mathematical competence. Although any special techniques you need are taught in this module, it would be helpful if you were familiar with differential equations and matrices. To help determine whether you are adequately prepared for this module try our Diagnostic Quiz.

Register

You may need to apply for some payment or funding options earlier. Please check the Fees and Funding information or contact us for information.

This module is expected to start for the last time in October 2018.

Additional Costs

Study costs

There may be extra costs on top of the tuition fee, such as a laptop, travel to tutorials, set books and internet access.

Ways to pay for this module

Open University Student Budget Account

The Open University Student Budget Accounts Ltd (OUSBA) offers a convenient 'pay as you go' option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that The Open University works exclusively with OUSBA and is not able to offer you credit facilities from any other provider. All credit is subject to status and proof that you can afford the repayments.

You pay the OU through OUSBA in one of the following ways:

Register now, pay later – OUSBA pays your module fee direct to the OU. You then repay OUSBA interest-free and in full just before your module starts. 0% APR representative. This option could give you the extra time you may need to secure the funding to repay OUSBA.

Pay by instalments – OUSBA calculates your monthly fee and number of instalments based on the cost of the module you are studying. APR 5.1% representative.

Employer sponsorship

Studying with The Open University can boost your employability. OU qualifications are recognised and respected by employers for their excellence and the commitment they take to achieve one. They also value the skills that students learn and can apply in the workplace.

More than one in ten OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the qualification you’ve chosen is geared towards your job or developing your career, you could approach your employer to see if they will sponsor you by paying some or all of the fees.

Your employer just needs to complete a simple form to confirm how much they will be paying and we will invoice them.

You won’t need to get your employer to complete the form until after you’ve chosen your modules.

Credit/debit card

You can pay part or all of your tuition fees upfront with a debit or credit card when you register for each module.

Mixed payments

We know that sometimes you may want to combine payment options. For example, you may wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an Open University Student Budget Account (OUSBA).

For more information about combining payment options, speak to an adviser or book a call back at a time that is convenient to you.

Please note: your permanent address/domicile will affect your fee status and therefore the fees you are charged and any financial support available to you. The fees and funding information provided here is valid for modules starting before 31 July 2016. Fees normally increase annually in line with inflation and the University's strategic approach to fees.

This information was provided on 31/03/2015.

What's included

Books, web-based software, website.

You will need

Calculator with the usual mathematical functions (exp, log, sin, cos), but not necessarily with statistical functions.

Computing requirements

You will need a computer with internet access to study this module as the study materials and activities are accessible via a web browser. Any other computer-based activities you will need to carry out, such as word processing, using spreadsheets, taking part in online forums, and submitting files to the university for assessment, are specified in the module materials. If any additional software is needed for these tasks it will either be provided or is freely available.

We recommend either of the following:

Windows desktop or laptop computer running Windows 7 or later operating system

A netbook, tablet, smartphone or Linux computer that supports one of the browsers listed below may be suitable. The screen size should be at least 1024 (H) x 768 (W) pixels. If you intend to use one of these devices please ensure you have access to a suitable desktop or laptop computer in case you are unable to carry out all the module activities on your mobile device.

We recommend a minimum 1 Mbps internet connection and any of the following browsers:

Internet Explorer 9 and above

Apple Safari 7 and above

Google Chrome 31 and above

Mozilla Firefox 31 and above.

Note: using the latest version for your browser will maximise security when accessing the internet. Using company or library computers may prevent you accessing some internet materials or installing additional software.

If you have a disability

This module may be very challenging if you have severely impaired sight. Almost all the texts contain detailed diagrams and there are a few data tables.

Adobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components (such as equations) may not be available or fully accessible using a screen reader and mathematical materials may be particularly difficult to read in this way.

If you have particular study requirements please tell us as soon as possible, as some of our support services may take several weeks to arrange. Find out more about our services for disabled students.